This paper presents strategies for the estimation and testing of risk difference and odds ratio under order restrictions. Estimates of the parameters of interest under order restrictions are obtained and subsequentlyusedintheestimationof risk difference, ratio of discordant probability and odds ratio. Also, estimates that make use of the marginal frequencies are obtained and studied. The variance and large sample bias of the estimates are given. Test procedures concerning risk difference and ratio of discordant probability are developed based on these order restricted estimates and their distributions. Power comparisons of the developed test procedures are given for sparse to moderate samples.

risk difference, binomial distribution, sample proportions, inequalities, estimation.